Multiple Positive Solutions of Singular Nonlinear Sturm‐Liouville Problems with Carathéodory Perturbed Term

Yuefeng Han, Xinguang Zhang, Lishan Liu and Yonghong Wu

Journal of Applied Mathematics, 2012, vol. 2012, issue 1

Abstract: By employing a well‐known fixed point theorem, we establish the existence of multiple positive solutions for the following fourth‐order singular differential equation Lu = p(t)f(t, u(t), u′′(t)) − g(t, u(t), u′′(t)), 0 0, i = 1,2, where L denotes the linear operator Lu : = (ru′′′)′ − qu′′, r ∈ C1([0,1], (0, +∞)), and q ∈ C([0,1], [0, +∞)). This equation is viewed as a perturbation of the fourth‐order Sturm‐Liouville problem, where the perturbed term g : (0,1)×[0, +∞)×(−∞, +∞)→(−∞, +∞) only satisfies the global Carathéodory conditions, which implies that the perturbed effect of g on f is quite large so that the nonlinearity can tend to negative infinity at some singular points.

Date: 2012
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https://doi.org/10.1155/2012/160891

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2012:y:2012:i:1:n:160891

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